182 
DR. E. P. PERMAN, DR. W. RAMSAY, AND MR. J. ROSE-INNES 
linear relation between the temperature and pressure, so that we may put 
p = hT - a, 
where h and a are functions of the volume only (‘ Phil. Mag./ voh 23, p. 436). From 
these two equations it is possible to eliminate the temperature, and we obtain 
p — h + 
cja 
h • 
Thus we see that for constant volumes E may be expi’essed as a linear function 
of p ; the next step is evidently to find the value of g/h. For this purpose the 
isochoral diagram was employed; a straight edge was laid so as to pass as near 
as might be to the drawn points, and the slope of this edge was then determined ; 
this slope gave the value of g. To obtain h nothing more was needed than to use 
the values given in Pamsay and Young’s paper [loc. cit., p. 441). On calculating 
the value of gjb for various volumes, it was found to be nearly constant; such 
deviations as existed were not arranged in any orderly manner, but occurred some¬ 
times to one side and sometimes to another, as if fluctuatino’ about a mean value. It 
appeared as if gjh = 11/9 might be taken as a fair mean between all the values 
obtained. We may therefore put 
u 7 L 11 
E = -j, - h + JO., 
and this leads to the equation 
V~ = 1631 — f{v), 
where /{ v ) is a function of v only. In order to determine the value of f { r ), the 
above was written 
f { v ) = 1631 jjy — Vh 
Keeping the volume constant, and changing the temperature, this equation gives 
values of_/(r) differing slightly from one another; the arithmetical mean was chosen 
as giving the value of f{v) for that particular volume. In this way /(?^) was deter¬ 
mined for a large number of volumes, and it was found that its values could be 
approximately represented by means of the empirical formula 
, 785,300,000 317,700,000 3,114,000,000 
f{0 = — ^55 - jr, -- 
The above formula was selected from a large number that were tried, and it 
repjroduced the found values of f{v) fairly well, but it is not suggested as being 
anything more than an empirical formula. Unfortunately the Kinetic Theory of 
Gases is not sufficiently advanced to enable us to form any d prion notion as to 
